1,414 research outputs found
Computing Topology Preservation of RBF Transformations for Landmark-Based Image Registration
In image registration, a proper transformation should be topology preserving.
Especially for landmark-based image registration, if the displacement of one
landmark is larger enough than those of neighbourhood landmarks, topology
violation will be occurred. This paper aim to analyse the topology preservation
of some Radial Basis Functions (RBFs) which are used to model deformations in
image registration. Mat\'{e}rn functions are quite common in the statistic
literature (see, e.g. \cite{Matern86,Stein99}). In this paper, we use them to
solve the landmark-based image registration problem. We present the topology
preservation properties of RBFs in one landmark and four landmarks model
respectively. Numerical results of three kinds of Mat\'{e}rn transformations
are compared with results of Gaussian, Wendland's, and Wu's functions
Convergence rates in expectation for Tikhonov-type regularization of Inverse Problems with Poisson data
In this paper we study a Tikhonov-type method for ill-posed nonlinear
operator equations \gdag = F(
ag) where \gdag is an integrable,
non-negative function. We assume that data are drawn from a Poisson process
with density t\gdag where may be interpreted as an exposure time. Such
problems occur in many photonic imaging applications including positron
emission tomography, confocal fluorescence microscopy, astronomic observations,
and phase retrieval problems in optics. Our approach uses a
Kullback-Leibler-type data fidelity functional and allows for general convex
penalty terms. We prove convergence rates of the expectation of the
reconstruction error under a variational source condition as both
for an a priori and for a Lepski{\u\i}-type parameter choice rule
CANVAS: case report on a novel repeat expansion disorder with late-onset ataxia
This article presents the case of a 74-year-old female patient who first developed a progressive disease with sensory neuropathy, cerebellar ataxia and bilateral vestibulopathy at the age of 60 years. The family history was unremarkable. Magnetic resonance imaging (MRI) showed atrophy of the cerebellum predominantly in the vermis and atrophy of the spinal cord. The patient was given the syndromic diagnosis of cerebellar ataxia, neuropathy, vestibular areflexia syndrome (CANVAS). In 2019 the underlying genetic cause of CANVAS was discovered to be an intronic repeat expansion in the RFC1 gene with autosomal recessive inheritance. The patient exhibited the full clinical picture of CANVAS and was tested positive for this repeat expansion on both alleles. The CANVAS is a relatively frequent cause of late-onset hereditary ataxia (estimated prevalence 5â13/100,000). In contrast to the present patient, the full clinical picture is not always present. Therefore, testing for the RFC1 gene expansion is recommended in the work-up of patients with otherwise unexplained late-onset sporadic ataxia. As intronic repeat expansions cannot be identified by next generation sequencing methods, specific testing is necessary
Necessary conditions for variational regularization schemes
We study variational regularization methods in a general framework, more
precisely those methods that use a discrepancy and a regularization functional.
While several sets of sufficient conditions are known to obtain a
regularization method, we start with an investigation of the converse question:
How could necessary conditions for a variational method to provide a
regularization method look like? To this end, we formalize the notion of a
variational scheme and start with comparison of three different instances of
variational methods. Then we focus on the data space model and investigate the
role and interplay of the topological structure, the convergence notion and the
discrepancy functional. Especially, we deduce necessary conditions for the
discrepancy functional to fulfill usual continuity assumptions. The results are
applied to discrepancy functionals given by Bregman distances and especially to
the Kullback-Leibler divergence.Comment: To appear in Inverse Problem
Iteratively regularized Newton-type methods for general data misfit functionals and applications to Poisson data
We study Newton type methods for inverse problems described by nonlinear
operator equations in Banach spaces where the Newton equations
are regularized variationally using a general
data misfit functional and a convex regularization term. This generalizes the
well-known iteratively regularized Gauss-Newton method (IRGNM). We prove
convergence and convergence rates as the noise level tends to 0 both for an a
priori stopping rule and for a Lepski{\u\i}-type a posteriori stopping rule.
Our analysis includes previous order optimal convergence rate results for the
IRGNM as special cases. The main focus of this paper is on inverse problems
with Poisson data where the natural data misfit functional is given by the
Kullback-Leibler divergence. Two examples of such problems are discussed in
detail: an inverse obstacle scattering problem with amplitude data of the
far-field pattern and a phase retrieval problem. The performence of the
proposed method for these problems is illustrated in numerical examples
Sparse Regularization with Penalty Term
We consider the stable approximation of sparse solutions to non-linear
operator equations by means of Tikhonov regularization with a subquadratic
penalty term. Imposing certain assumptions, which for a linear operator are
equivalent to the standard range condition, we derive the usual convergence
rate of the regularized solutions in dependence of the noise
level . Particular emphasis lies on the case, where the true solution
is known to have a sparse representation in a given basis. In this case, if the
differential of the operator satisfies a certain injectivity condition, we can
show that the actual convergence rate improves up to .Comment: 15 page
A combined first and second order variational approach for image reconstruction
In this paper we study a variational problem in the space of functions of
bounded Hessian. Our model constitutes a straightforward higher-order extension
of the well known ROF functional (total variation minimisation) to which we add
a non-smooth second order regulariser. It combines convex functions of the
total variation and the total variation of the first derivatives. In what
follows, we prove existence and uniqueness of minimisers of the combined model
and present the numerical solution of the corresponding discretised problem by
employing the split Bregman method. The paper is furnished with applications of
our model to image denoising, deblurring as well as image inpainting. The
obtained numerical results are compared with results obtained from total
generalised variation (TGV), infimal convolution and Euler's elastica, three
other state of the art higher-order models. The numerical discussion confirms
that the proposed higher-order model competes with models of its kind in
avoiding the creation of undesirable artifacts and blocky-like structures in
the reconstructed images -- a known disadvantage of the ROF model -- while
being simple and efficiently numerically solvable.Comment: 34 pages, 89 figure
PDEs for tensor image processing
Methods based on partial differential equations (PDEs) belong to those image processing techniques that can be extended in a particularly elegant way to tensor fields. In this survey paper the most important PDEs for discontinuity-preserving denoising of tensor fields are reviewed such that the underlying design principles becomes evident. We consider isotropic and anisotropic diffusion filters and their corresponding variational methods, mean curvature motion, and selfsnakes. These filters preserve positive semidefiniteness of any positive semidefinite initial tensor field. Finally we discuss geodesic active contours for segmenting tensor fields. Experiments are presented that illustrate the behaviour of all these methods
Endothelin-1 Predicts Hemodynamically Assessed Pulmonary Arterial Hypertension in HIV Infection.
BackgroundHIV infection is an independent risk factor for PAH, but the underlying pathogenesis remains unclear. ET-1 is a robust vasoconstrictor and key mediator of pulmonary vascular homeostasis. Higher levels of ET-1 predict disease severity and mortality in other forms of PAH, and endothelin receptor antagonists are central to treatment, including in HIV-associated PAH. The direct relationship between ET-1 and PAH in HIV-infected individuals is not well described.MethodsWe measured ET-1 and estimated pulmonary artery systolic pressure (PASP) with transthoracic echocardiography (TTE) in 106 HIV-infected individuals. Participants with a PASP â„ 30 mmHg (n = 65) underwent right heart catheterization (RHC) to definitively diagnose PAH. We conducted multivariable analysis to identify factors associated with PAH.ResultsAmong 106 HIV-infected participants, 80% were male, the median age was 52 years and 77% were on antiretroviral therapy. ET-1 was significantly associated with higher values of PASP [14% per 0.1 pg/mL increase in ET-1, p = 0.05] and PASP â„ 30 mmHg [PR (prevalence ratio) = 1.24, p = 0.012] on TTE after multivariable adjustment for PAH risk factors. Similarly, among the 65 individuals who underwent RHC, ET-1 was significantly associated with higher values of mean pulmonary artery pressure and PAH (34%, p = 0.003 and PR = 2.43, p = 0.032, respectively) in the multivariable analyses.ConclusionsHigher levels of ET-1 are independently associated with HIV-associated PAH as hemodynamically assessed by RHC. Our findings suggest that excessive ET-1 production in the setting of HIV infection impairs pulmonary endothelial function and contributes to the development of PAH
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